You can set a zero fee in BTC, it is regarded as a dust. The transaction can confirm in the case you have asked about but, if it will confirm is dependant upon the transaction broadcast by the individual nodes, the node may not accept a transaction with fees below a particular level, particularly if that nodes mempool is rather full, and it depends on if miners will include the transaction in a block.

Even if in the past there have been zero fee transactions included in blocks, I would not risk it.